Various artifacts plague the medical images obtained by CT scanners. The scientists and engineers who develop such equipment are continuously attempting to reduce the image artifacts. An example of such artifacts is the polychromatic artifact indentified by cupping and streaks in images. An example of a system for minimizing artifacts is shown in U.S. Pat. No. 4,217,641 which uses an iterative post-reconstruction method to reduce the level of the artifacts. As another example, there is the paper entitled "A Simple Computational Method for Reducing Streak Artifacts in CT Images", by G. Henrich, in Computed Tomography, Vol. 4, 1981 which describes an algorithm that can be used to remove streaks such as those caused by partial volume artifacts. Ring artifacts in rotational CT scanners are well known. U.S. Pat. No. 4,352,020 uses a calibration method to reduce such artifacts.
U.S. Pat. Nos. RE. 30,947 and 4,075,492 teach reordering the divergent rays of a fan beam CT scanner into parallel rays. However the spacings between the reordered rays are not laterally equal. This causes "cupping" artifacts. To remove these artifacts the RE 30947 Patent presents an interpolation method that generates parallel projections of equal spacing between samples from unequally spaced reordered projections. U.S. Pat. No. 4,570,224 which issued on Feb. 11, 1986 and is assigned to the assignee of this invention, gives additional methods for reducing the cupping artifacts by using other interpolation techniques.
A problem encountered with both the above interpolation methods is that while they do succeed in reducing the cupping artifacts the interpolation methods produce structured noise in the reconstructed images. The noise has the form of partial streaks tangent to several circles on the image, as if caused by a rotational noise sprinkler. As a special case, these streaks can be radial (when the circle is of a very small radius).
The cause of the artifact generally is that the signal output from each detector contains data and noise. Since the reconstruction system is linear the effect of the input noise can be analyzed while the data is ignored. Suppose an interpolated (output) sample is calculated from two input samples by linear interpolation, the noise of the output sample depends on the interpolation coefficients.
The noise is attenuated, for example, by a factor of 0.7071 (when both coefficients are 0.5) and by a factor of 1 (when one coefficient is 1 and the other is 0). As a consequence of the interpolation, the interpolated data (the parallel projection) will have points of "Low Noise" (corresponding to the attenuation factor 0.7071), and points of "High Noise" (corresponding to the attenuation factor (1) in which the noise level is not changed. After filtration and back-projection, streaks of noise tangent to a circle corresponding to "High Noise" points appear in the reconstructed image.
Similar noise artifacts can occur when interpolation is performed between samples of the same detector; i.e, vertical interpolation, as distinguished from horizontal interpolation where the interpolation is between the samples of a projection. In CT scanners such vertical interpolations have been employed as a step in reordering divergent projections to (unequally spaced) parallel projections. See, for example, the book "Image Reconstruction from Projections", by Gabor T. Herman, Academic Press, 1980. Another case where vertical interpolation has been used is when the reordered projections are not perfectly parallel such as for example, in Dual Focal Spot Scanners (see Patent application Ser. No. 518,121 filed on July 7, 1983 and assigned to the assignee of this invention).
In all the above examples of the use of interpolation, if the interpolation coefficients used for calculating samples are different for adjacent samples in the obtained projection, but are identical for the same sample in all (or in part of) the projections, the noise is attenuated by different factors. Hence, the projections will contain non-uniform noise which can cause artifacts in the image as explained earlier. Accordingly there is a need for systems and/or method for minimizing noise artifacts generated when interpolation methods change normally uniform noise distribution to non-uniform noise distribution.